基于限定误差界的三角网格简化

Triangular Mesh Simplification Based on Bounded Error

提出了以限定误差界为准则,运用顶点去除法简化三角网格的算法.首先对所有顶点按照曲率大小进行排序,形成按照降序排列的顶点集,顶点越靠后,其周围局部曲率越小.对即将去除的顶点,计算该点周围区域在该点去除前后最小包围盒高度的变化量E,以变化量E为顶点去除的限制条件.这样既可设定简化比率,又可以控制简化误差.对顶点去除后,还需对因此形成的多边形区域进行网格重建,填补空洞.实验证明,该算法可以实现简化效率和简化误差的双重控制,简化效果好.

An algorithm of triangular mesh simplification with vertex culling is proposed. The method is based on bounded error. First, the vertexes are sequenced according to their curvature to form a descending order vertex array. The rearer vertex has smaller local curvature. Then, for a vertex to be deleted, the height of the local area of bounding box is calculated. And the reduction of the height after vertex culling is taken as the condition of vertex culling. Thus, its simplification ratio and error can be controlled. After vertex culling, triangular mesh reconstruction is conducted at the generated polygon to fill up hollows formed in the above steps. Experimental results show that the algorithm well balances the simplification efficiency and simplification error.